The meeting host has the option to toggle the attendee names on or off. 

When the attendees are visible the button will have a red X over it. 

Click it and the attendee names are hidden from view,

When off the attendee list is minimised and the attendee names beside each pin is also hidden.

To unhide the list of attendees simply click the button again

This option affects all attendees. If the host hides attendee names then no attendee sees anyone else's name unless the host chooses to unhide names.